DBD-NME: where do we stand ?

1. DBD-NME: where do we stand ? Osvaldo Civitarese University of La Plata. *some of the results presented in this talk have been obtained in collaboration with J. Suhonen. Univ. of Jyvaskyla .

2. Topics and Motivations Parameters and dependence of the nuclear matrix elements upon them. BCS, the QRPA and beyond. Short range correlations. Form factors Systematics of spin-isospin effects. Results. Conclusions.

3. -Nuclear structure effects on the matrix elements governing the mass sector of the neutrinoless double beta decay (g_pp-dependence) -Effective parameters: single-beta decay and double beta decay? two-neutrino or zero-neutrino modes? -Universality (if any) of the matrix elements * as a rule: if a certain approximation does not work in a simple model then there is certainly a problem with it in realistic cases.

4. v2 P P P e2 v1 P e2 e1 e1 HW HW HW HW v=v ? N N N N 2 neutrinos 0 neutrinos

5. Schematic view A(N-1,Z+1) A(N,Z) A(N-2,Z+2)

6. 2-neutrinos mode A(N,Z) A(N-2,Z+2)+2 electrons +2 neutrinos a) Lepton number is conserved b) Suppressed by kinematics (four leptons in the final state) c) Independent of neutrino properties

7. 0-neutrinos mode A(N,Z) A(N-2,Z+2)+2 electrons lepton number is not conserved favour by kinematics (two leptons in the final state)

8. Basic Information (consistency test) • Single beta decay and EC transitions • Energy spectra, electromagnetic transitions • Particle transfer and charge exchange (3He,t),(p,n) data. Practical rule: The information obtained by “theoretical reproducing” a single DBD transition does not mean anything, unless these related observables are also reproduced.

9. Need some experiments to help test calculations: a) pair transfer reactions connecting the states, b) 1-N transfer for occupation of valence orbits. • These would test theoretical descriptions of the relevant nuclei, and the range of uncertainties for (02) could be narrowed down. . • The importance of pairing to (02) needs to be better understood and pair transfers measured.

11. Some results obtained by John Schiffer et al.

13. Summary about BCS and vacuum effects • The experimental information is against the use of different BCS vacuum states, for the initial and final ground states involved in DBD transitions. • The experimental information is also against protron-neutron pairing correlations, as they have been used in some DBD calculations.

14. G_pp dependence • Transformation from the single-particle to the quasi-particle basis (particle number is lost, isospin symmetry is lost) • QRPA basic equations • Inclusion of pair terms of the residual quasiparticle interactions(isospin symmetry is lost) • Effective parameters of the interactions (spurious effects are introduced) • Mean field terms and residual interactions (couplings)

24. About the “ g_pp” problem • The use of two neutrino DBD fitted nuclear matrix elements does not relate to realistic values of neutrinoless DBD NME. • Neutrinoless DBD NME almost insensitive to particle-particle correlations.

25. Short Range Correlations • Effects due to the finite size of the nucleons, with reference to the momentum q (neutrino momentum) • Since q is or the order of 150-200 MeV/c short range correlation effects are expected to be operative at distances of the order of 1fm • Abnormaly large correcctions (of the order of two) have been reported in the literature, in contrast to smaller effects found in shell model calculations.

26. Jastrow correlations

28. On the use of Jastrow correlations • Details will be presented by Jouni Suhonen in his talk, for the sake of this presentation it would be enough to say that the use of Jastrow factors greatly overstimates the effect of short range correlations upon DBD-NME.

29. Beyond the QRPA -Inclusion of terms which go beyond the quasi-boson approximation: the procedure is not supported by self-consistency requirements and it introduces spurious effects. -Among the attempts: “fully renormalized qrpa”

34. Symmetries Isospin violations (mean field effects) 1)Mean field approximations (like BCS) break isospin and number symmetries. 2)The QRPA also break these symmetries, but in a different way. 3)Both mechanisms are not coupled.

39. Spin-isospin excitations • Detailed experimental information available (3He,t) (p,n). • Relevance of spin and isospin excitations in high precision nuclear structure studies, like nuclear double beta decay and neutrino-nucleus scattering. • Failure of the naive BCS approach, due to phase transitions, in the vecinity of closed shells.

40. Theoretical tools • Degrees of freedom: Isovector and Isoscalar Pairing and Gamow-Teller Excitations. • Coupling between them. • Renormalization of transitions within the same shell.

42. Mixing Between Pairing and GT phonons

43. Renormalized Matrix Elements

44. Distribution of Intensities

46. The method has the potential to go beyond the shell model approach since states up to seven particles and five holes have been included in the calculations. • Renormalization effects, which cannot be accounted for by using state independent effective charges, are explained by considering the coupling of Pairing and Gamow-Teller phonons.

47. Spurious roots The QRPA do have spurious roots (a zero energy root) which originates in the quasiparticle pair terms of symmetry operators (like number, isospin, or angular momentum in the deformed case). They represent collective rotations in the space of the symmetry variables. The root is coupled to the “intrinsic” roots, sometimes it is mistaken as a real intrinsic root.

50. Results Standard elements are: -WS or harmonic oscillator potentials. -Effective interactions constructed from one pion exchange potentials. -Gap parameters adjusted to reproduce odd-even mass differences around the double beta decay systems.